On the reduction of multivariate quadratic systems to best rank-1 approximation of three-way tensors

被引：4

作者：

da Silva, Alex P. ^{[1
]}

Comon, Pierre ^{[1
]}

de Almeida, Andre L. F. ^{[2
]}

机构：

[1] CNRS UMR2016, GIPSA Lab, Grenoble Campus,BP-46, F-38402 St Martin Dheres, France

[2] Univ Fed Ceara, Dept Teleinformat Engn, Campus Pici S-N,CP 6005, BR-60455970 Fortaleza, CE, Brazil

来源：

APPLIED MATHEMATICS LETTERS | 2016年 / 62卷

基金：

欧洲研究理事会;

关键词：

Quadratic systems; Tensor; Rank-1; approximation; DECOMPOSITION; OPTIMIZATION; CONVERGENCE; RELAXATIONS;

D O I：

10.1016/j.aml.2016.06.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we show that a general quadratic multivariate system in the real field can be reduced to a best rank-1 three-way tensor approximation problem. This fact provides a new approach to tackle a system of quadratic polynomials equations. Some experiments using the standard alternating least squares (ALS) algorithm are drawn to evince the usefulness of rank-1 tensor approximation methods. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：9 / 15

页数：7

共 38 条

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